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We investigate the charge excitations of a Weyl semimetal in the axioniccharge density wave (axionic CDW) state. While it has been shown that thetopological response (anomalous Hall conductivity) is protected against the CDWstate, we find that the long wavelength plasmon excitation is radicallyinfluenced by the dynamics of the CDW order parameter. In the normal state, weshow that an undamped collective mode should exist at q~Q_(CDW) if there is anattractive interaction favoring the formation of the CDW state. The undampednature of this collective mode is attributed to a gap-like feature in theparticle-hole continuum at q~Q_(CDW) due to the chirality of the Weyl nodes,which is not seen in other materials with CDW instability. In the CDW state,the long wavelength plasmon excitations become more dispersive due to theadditional interband scattering not allowed in the normal state. Moreover,because the translational symmetry is spontaneously broken, Umklapp scattering,the process conserving the total momentum only up to nQ_(CDW) with n an integerand Q_(CDW) the ordering wave vector, emerges in the CDW state. We find thatthe plasmon excitation couples to the phonon mode of the CDW order via theUmklapp scattering, leading to two branches of resonant collective modesobservable in the density-density correlation function at q~0 and q~Q_(CDW).Based on our analysis, we propose that measuring these resonant plasmon-axionexcitations around q~0 and q~Q_(CDW) by the momentum-resolved electron energyloss spectroscopy (M-EELS) could serve as a reliable way to detect the axionicCDW state in Weyl semimetals.

Resonant Plasmon-Axion Excitations Induced by Charge Density Wave Order in Weyl Semimetal